In the biopharmaceutical industry, process chromatography using packed-bed columns is a key component in the manufacture of complex biological products. In order to ensure product quality and performance (e.g., biological activity), a high packing quality is required. Accordingly, packing quality must be monitored and packed-bed columns having an unacceptable packing quality must be repacked or replaced.
Conventionally, three numeric parameters, namely, the number of plates per column (N), height equivalent to a theoretical plate (HETP), and asymmetry (As), are used to describe the quality of a packed-bed column. These parameters are obtained by performing pulse injections experiments or so-called HETP runs to assess the degree of dispersion of an injected pulse of a non-adsorbed solute.
In accordance with the pulse injection method for assessing packing quality, a well-packed column should have a low HETP value (e.g., less than 0.1 cm). A concept derived from N, HETP provides a measure of broadening in relation to the distance a sample zone has traveled in a chromatography column. A sample zone is the band of a sample in the column, which appears as a peak when it exits the column and is monitored by a detector (analyzer) that corresponds to a certain property of the sample at the column outlet. The mathematical definitions of N and HETP are:N=VR2/σ2  (1), andHETP=L/N  (2),where VR is a retention volume, which is defined as the volume delivered from the time when half the sample mass is applied to the column to the time when half the sample mass has exited from the column, σ2 is the variance of the exit volume distribution, and N is a dimensionless number. L is the column length (or height).
The injected tracer solution in the injected pulse method is assumed to be a Dirac pulse, which has a height of C0 (the initial tracer concentration) and, relative to the column volume, an infinitesimal width. The initial condition corresponds to a column containing only the mobile and stationary phase in equilibrium but without any sample. The injected pulse method also assumes that the distribution of the exit volume of the tracer in the pulse follows, or closely follows, a normal (e.g., Gaussian) distribution curve. Thus, the calculation of N is determined by just three data points from the concentration-volume curve derived during a pulse injection experiment (e.g., the volumes at the peak and at the two points on the curve where the concentration of the tracer is half of the peak concentration). For a normal density function, the width of the curve at half peak height, W1/2, is equal to 2σ(21n2)1/2. Therefore,σ=W1/2/(2(21n2)1/2  (3).Consequently, the calculation of N is given by:N=VR2/(W1/2/(2(21n2)1/2)2  (4),N=VR2/(W1/22/(4(21n2)))  (5),N=5.545(VR/W1/2)2  (6).
The value of HETP is obtained by using equation (2) above.
The third parameter, As, used to describe the quality of a packed-bed column, reflects the nature of the peak broadening (e.g. fronting or tailing). As above, in the case of the pulse injection method, just three data points from the entire dataset obtained during a pulse injection experiment are used to determine the value As. This value is calculated by taking the ratio (at 10 percent of the peak height) of the distance between the peak apex and the back side of the chromatographic curve to the distance between the peak apex and the front side of the chromatographic curve. Accordingly, an As value greater than 1 is a tailing peak, while an As value less than 1 is a fronting peak. A well-packed column is assumed to have an As value close to unity.
Because there are frequently situations where the peaks from pulse injection experiments or HETP runs are not Gaussian, the N, HETP, and As values calculated in accordance with the pulse injection method often do not accurately describe the efficiency or packing quality of a column. This is especially true for large process chromatography columns, which routinely give peaks that do not fit a Gaussian distribution. In fact, a calculation that is based on a Gaussian distribution may be insensitive to changes in bed condition or defects in column packing. The reason for this is that if deviations occur somewhere in a transition other than at the few data points used in the calculation, the deviations will not be detected. For the same reason, the pulse injection method is not robust because noise occurring at these critical points will be weighted heavily and lead to incorrect calculations.
In addition to the above noted shortcomings, there are also practical and economical reasons that make the pulse injection method for determining packing quality poorly suited for use in large-scale process chromatography. For example, when running a pulse injection experiment, the volume of the pulse directly affects the results. Since it is difficult to accurately introduce a small pulse into a large column, the reproducibility of HETP runs at the production scale is typically low, especially where subtle changes in the column are concerned. This weakness can render the parameters measured with the pulse injection method unsuitable for use with statistical process control. Furthermore, HETP runs are external to the manufacturing process, and the parameters derived from them are not direct measures of the efficiency or packing quality of the columns when the columns are actually used during the manufacturing process. Column conditions can change between a HETP run and an actual manufacturing process run. When the change is sufficiently large, it can have potentially catastrophic effects on the ensuing process chromatography. Finally, the pulse injection method requires HETP runs to be performed on a regular basis to check the efficiency of the column. These HETP runs consume process resources and can cause delays in production.
What are needed are new monitoring systems and methods that overcome the deficiencies noted above.